Question

Each interior angle of a regular polygon measures 156°. how many sides does the polygon have?

Answer 1

the angle interior formula is
each interior angle=
`((n-2)180)/(n)` where n=number of sides
subsitute156= [tex] \frac{(n-2)180}{n} [\tex]
multiply both sides by n
156n=(n-2)180
divide both sides by 180
13/15 times n=n-2
multiply both sides by 15 to clear fraction
13n=15n-30
subtract 13n from both sides
0=2n-30
add 30 to both sides
30=2n
divide 2
15=n

it has 15 sides

Answer 2

we know that each angle in a regular polygon is given by the formula
angle=(180)(n-2)/n where is number of sides
we actually have the angle, so we can write
156=(180)(n-2)/n
156*n=180 *(n-2)
furthermore
156n=180n-360
360=180n-156n
360=24n
n=360/24
n=15
this is a polygon with 15 sides